Bipolar transistors are known to possess positive temperature coefficient for current gain, implying that the current gain increases as temperature increases. This is accompanied by a decrease in base-emitter voltage at elevated temperatures. Both of these factors combine to limit the performance of bipolar transistors, both at room temperature and at high temperatures. The increase in current gain is especially problematic for the design of output amplifiers, where the transistors are designed to operate very close to the extreme Ic and Vce limits. In many instances, the increase in current gain at high temperature results in over-designing at room temperature. Increase in current gain accompanied by a reduction is collector-emitter breakdown voltage BVceo, which is approximated by the ratio of collector-base breakdown voltage divided by the current gain raised to a power. Since BVceo is a design parameter, a certain minimum value of this quantity has to be guaranteed by design at all temperatures. In order to meet the minimum value of current gain at the lowest temperature, a higher value of current gain has to be tolerated at the higher temperatures. As a result, the minimum value of the BVceo is recorded at the highest temperature. This results in the design of the transistor with the value of BVceo greater than the minimum required at room temperature, which leads to the sub-optimal design of the transistor at the room temperature, since BVceo has a direct correlation with the cut off frequency of the transistor, which is the determining parameter for the high frequency performance of the transistor.
The physics behind this phenomenon of increase in current gain with temperature is well researched and understood. It has been proposed that the current gain tends to increase at high temperature because the temperature coefficients of the collector current and the base current have varying temperature coefficients. While the collector current is inversely proportional to the base Gummel number, the base current is inversely proportional to the emitter Gummel number to the first order. (Base Gummel number is the integral of the active dopants in the neutral base.) Due to the higher doping in the emitter region, greater band gap narrowing takes place in the emitter region as compared to the base region. This phenomenon results in a positive exponential coefficient for the current gain with activation energy equal to the difference in the band gap narrowing in the emitter region with respect to the base region. The reverse is true at low temperatures, i.e., current gain decreases as temperature decreases which also poses limits on the operation of bipolar transistors. The extent of band gap narrowing has been documented extensively in the industry (see, for example, J. C. S Woo and J. D. Plummer, “Optimization of silicon bipolar transistors for high current gain at low temperatures.” IEEE Trans Electron Devices, Vol. 35, No. 8, August 1988, pp. 1311-1319). The resulting band gap narrowing in degenerately doped n and p type silicon has been empirically shown to follow the relationship:ΔEg=3.74×10−3*log((N/N0)5+1),where N is the doping density, No is an empirical constant, equal to 9×1017/cm3 for N type silicon and 1×1017/cm3 for P type silicon. Assuming the doping in the emitter of 1×1020/cm3 and base doping of 2×1017/cm3, the resulting band gap lowering in the emitter is 37.4 meV, and the band gap narrowing in the base is a fraction of a mV, and a difference in band gap narrowing of 37 eV between emitter and base. The current gain temperature coefficient is also approximated by this activation energy, i.e.,β∝exp(0.037/kT)
Using this expression, the current gain increase from 300 Kelvin (27 degrees Celsius) to 400 Kelvin (127 degrees Celsius) is found to be a factor of 1.42, i.e., an increase of 42% over this temperature range.
The present invention is directed at overcoming this limitation.